An X-ray CT apparatus acquires projection data by receiving an X-ray radiated from an X-ray source and transmitted through an object being examined, with an X-ray detector disposed on the opposite side of the X-ray source interposing the object therebetween. Upon acquiring the projection data, the X-ray source and the X-ray detector disposed to be opposite to each other interposing the object therebetween are revolved around revolving axis, and the projection data in different angles of rotation (phase) are collected. By reconstructing this projection data, the creation of the internal image of the object is attained in a non-destructive manner.
Such X-ray CT apparatuses are one of two kinds. One uses a single-array detector of which the detector elements are arranged one-dimensionally (line), and another kind uses a multi-array detector of which the detector elements are arranged two-dimensionally.
An imaging method in the simplest X-ray CT apparatus is the normal scanning method for creating an image by revolving an X-ray source and a detector around a revolving axis in a range of 2π, and the scanning range of the projection data acquired by this normal scanning method is 2π [rad].
On the other hand, since the above-mentioned fan beam or cone beam diverges centering around a central beam directed toward the revolving axis from the X-ray source, with regard to one beam directed toward the detector from the X-ray source, the same projection data (line integral) is measured twice during one revolution of the X-ray source and detector. Since such redundancy of data should be minimized to reduce the X-ray exposure, the imaging method for setting the scanning range at less than 2π is also adopted. As shown in FIGS. 14 (a) and (b), the beams are equivalent when the position of the X-ray source and the position of one detector element are switched, and by setting the maximum fan angle of the fan beam as 2γm as shown in FIG. 14 (c), the projection data of all beams necessary for the image reconstruction can be measured at the point of the X-ray source moving by π+2γm. This range is the minimum scanning range.
However if the image reconstruction as in the case of scanning range is 2π is carried out corresponding to the projection data obtainable from π+2γm scanning range, the image gets distorted and the image quality deteriorates. This is due to the phase range of data possible to perform back projection being different with respect to each pixel. In other words, for example, as shown in FIG. 15, in pixel p1 the data by which the phase range is more than π is used for the image reconstruction centering around pixel p1, but in pixel p2 only the data by which the phase range is less than π is used centering around pixel p2.
This means that the redundancy of the projection data is different depending on the pixel. This is illustrated in a sinogram in FIG. 16 to indicate projection data, by representing the fan angle (an angle formed by the central beam and the respective beams) γ on the horizontal axis and the revolving phase angle β on the vertical axis. In other words, FIG. 16 is a sinogram showing a minimum complete data set, and the upper and lower triangle portions denoted with diagonal lines are the data being redundant to each other.
As a method to solve the problem relating to the redundant data as mentioned above, it is suggested in Patent Document 1 to assign weight to, for example, a predetermined region of the projection data.
Patent Document: JP-A-2001-299738
With regard to weighting function w for the fan beam it generally is required to fulfill formula (1), and to fulfill formula (2) regarding weighting function w for the parallel beam.
                    [                  Formulas          ⁢                                          ⁢          1                ]                                                                                  ∑                          n              =              0                        ∞                    ⁢                                          ⁢                      {                                          w                ⁡                                  (                                                            β                      +                                              2                        ⁢                        π                        ⁢                                                                                                  ⁢                        n                                                              ,                    γ                                    )                                            +                              w                ⁡                                  (                                                            π                      +                      β                      +                                              2                        ⁢                        γ                                            +                                              2                        ⁢                        π                        ⁢                                                                                                  ⁢                        n                                                              ,                                          -                      γ                                                        )                                                      }                          =        1                            (        1        )                                                      ∑                          n              =              0                        ∞                    ⁢                                          ⁢                      {                                          w                ⁡                                  (                                      β                    +                                          2                      ⁢                      π                      ⁢                                                                                          ⁢                      n                                                        )                                            +                              w                ⁡                                  (                                      π                    +                    β                    +                                          2                      ⁢                      π                      ⁢                                                                                          ⁢                      n                                                        )                                                      }                          =        1                            (        2        )            
However, while these weighting functions can be applied to the image reconstruction from a minimum complete data set (π+2γm of scanning range) or the full-scanning data set (2π of scanning range), they are not applicable to the image reconstruction from a data set in which the scanning range is between these ranges. To solve this problem, a weighting function to be applied to data sets of intermediate-range is suggested in Patent Document 1. Here, as shown in FIG. 17, by setting and using virtual fan angle  which is not dependent on the actual and physical maximum fan angle, the reconstruction from the projection data with a scanning range of π+2γm˜2π is achieved.
However, these weighting functions suggested in the past are not applicable to the scanning range of over 2π. Since the weighting function to apply for the scanning range changes to a different one at the point of the scanning range being over 2π, the image quality such as noise quantity or artifact intensity will also be different between the result of the reconstruction from the range narrower than 2π and the result of reconstruction from the range wider than 2π.
Also, on the virtual sinogram shown in FIG. 17, in the case that the different weight is assigned to the two triangles in the revolving phase direction, the configuration of the weighting function turns out to be a trapezium, triangle or the deformed non-linear shapes thereof, and the configuration gets closer to a triangle from a trapezium as the scanning range draws closer to 2π. This means that the region of which the weighting factor is less than 1 increases as the scanning range gets closer to 2π, and the data contribution ratio decreases significantly compared to the case that the scanning range is 2π and the weighting factor of all the range thereof is 1, which can lead to a notable increase of noise (i.e. a decrease of SNR).
Another common problem is that the imaging noise decreases as the imaging data amount to be used for the reconstruction processing increases. In other words, the imaging noise decreases as the projection data width (projection data angle using for back-projection) increases. However, acquiring a wide phase range means the redundant imaging of the same place as shown in FIG. 18, which accompanies the decrease of the measurement through-put (spiral pitch, beam pitch and table feeding speed). In this way, the decrease of the image noise and the reduction of imaging time are in trade-off relationship to each other, and the relationship between them can be inappropriate depending on the imaging purposes.
On the other hand, in order to reduce the contradiction of data by motion movement and the deterioration of image quality caused by it, the arithmetic addition of the same data is performed. More specifically, for example in normal scanning, if there is no movement of the object being examined during one revolution of the X-ray source and detector, the projection data of imaging start-time phase (β=0) coincides with the projection data of imaging end-time phase (β=2π). However, since it is impossible to completely remove the motions such as heart beats or blood flow, as shown in FIG. 19 (a)˜(c) a discontinuity (data inconsistency) is generated in both projection data 51 and 52 which leads to a notable deterioration of image quantity such as streak artifacts 53 and 54. This discontinuity can be reduced by acquiring the identical data of imaging start time and imaging end time, and performing weighted addition between them. However, the assignment of a small weight causes a decrease of data contribution rate that leads to a decrease of SNR. In this way, the amount of image noise and corrective effect of discontinuity are in a trade-off relationship, and this relationship can be inappropriate in some situations.